Menagerie — The Trial of Spock

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Two main interests drive my work as a theorist. The first is a concern about pulse, how we sense it, and how we perceive rhythm when pulse is absent or transient. The second regards how music might be shaped by ideology—especially on questions related to a sense wholeness or unity in a musical expression. 


Pulse is maybe the simplest kind of musical experience, and much has been said about how we perceive it. My work is concerned with what’s going on when, in a musical experience, we have strong or weak urges to tap our feet, or experience an inexplicable loss or gain of “pulse.” Composers are often interested in complicating the experience of pulse, or resisting it, often through complications of the arithmetic of meters, beats, and subdivisions. But few have investigated how mathematical complexity relates to perceptual complexity in rhythm. To study this, I conduct empirical studies of pulse perception: “Perceiving and distinguishing…” below is my most recent and extensive attempt to approach this question.

Perceiving and distinguishing simple timespan ratios without metric reinforcement [.pdf file, 2 MB].

Journal of New Music Research 36/4 (December 2007), 313-36. 

The article above asks how we hear ‘simplicity’ or ‘harmonicity’ in a pair of timespans, especially when they are heard ‘by themselves’ and without a clear basis for expectation of how notes will mark time.^1

Answering this question requires us to separate out the very different (but perceptually influential) issue of “metric hierarchy”: how regularly-spaced streams of events form larger patterns in our minds. From Dowling’s (1973) landmark studies of stream segregation, Bregman’s (1990) landmark studies of ‘auditory scene analysis,’ along with empirical work by Idson & Massaro (1976), Andrew Gregory (1994), and Hasan Tekman (1995, 1997), I developed a methodolgy that allowed conflicting “cues”—changes on different dimensions of musical information—to compensate against one another in the determination of how listeners divide up groups of musical events into subgroups. By composing a variety of “degrees of separation” for a given rhythmic subgroup in a musical passage, I was able to trace changes in listeners’ confidence in pulse, as a function of the exposure of pulsed (but non-hierarchical) rhythms.

My second area of interest as a theorist connects with the first in one aspect of this experimental design. Because ‘grouping processes’ are multidimensional, the issue of how groups unify, and how we perceive them as ‘wholes’ of any kind, is complex. My interest in the potentially ideological roots of musical wholes, and their boundaries is amplified by the detailed attention I had to pay to the boundaries between streams, and the issue of when a rhythm is “complete.” Where are the potential dividing lines of one musical idea and another? Have all of them been explored well by composers? What factors (perceptual or otherwise) have tended to inform listeners’ interpretations of those boundaries?



My interest in musical form extends to a number of different short essays and papers. The most extensive work on the topic culminated in an article that is now the first chapter of an edited collection from the Search Journal of New Music and Culture.

[.zip file, 2.3 MB] Schoenberg’s ambivalent thought: subjectivity in ‘Du lehnest wider eine Silberweide…” In Cox, Biro, Takesugi, & Sigman, eds., Search Yearbook: The Second Century of New Music. New York: Edwin Mellen Press, 2011.

Since the chapter is lengthy, and because it begins with an overview of a fairly arcane debate in musicology, I like to offer some readers a broader introduction to it, explaining how I was motivated toward this particular research, and how it is related to some of my longer-term creative goals. 

In music we sometimes use the term “subject” to refer to a tune that’s introduced and then later transformed in a composition. Musical subjects are somewhat like literary subjects, in that both musical and literary compositions often develop and vary in ways that are anchored by a subject; the subject in both worlds is a kind of central figure, a kind of carrier of identity and of agency. Musical subject in the 19th century took front-seat roles in musical form, displacing the greater importance of harmonic schema in the late 18th century. The musicologist Carl Dahlhaus (1980) argues that “compositional economy”—a relatively small subject’s capacity to sustain a relatively large narrative—was among the highest values of composers like Liszt, Wagner, and Brahms, under the sway of a Romantic “cult of genius.” Small-scale melodic and harmonic materials thus stood at the center of a work, and were, in Wagner’s words, “pregnant and implicitous” if they managed to preside over a large form about them.^2

In many small essays, the composer and theorist Arnold Schoenberg (1923-1934, 1947, 1951) disagreed. European and American musicians in the early 20th century often considered Wagner on a par with Beethoven, but Schoenberg insisted that the post-Wagnerian ‘linear’ and ‘prosaic’ approach were inadequate: counterpoint” and difference, an advance sense of a gulf to cross between unrelated things … these formal dimensions of a work are indispensible. Schoenberg’s widely expanded notion of Gedanke, or musical thought/idea (somewhat like the Italian soggetto) effectively up-ends Wagner’s commonsensical idea that form is the consequence of melodic ideas and their implications…implying instead that ideas are the consequences of wholes. But he also reaffirms that when composers think about subjects, they are thinking about a kind of identity, a kind of figure that has to make its way in a world by distinguishing itself from, and within, its surroundings.

With that broader sense of the term “subject” in mind, and helped-along by Deleuze and Guattari’s (1972) critiques of literary and psychological subject in Anti-Oedipus: Capitalism and Schizophrenia, I have found, in the article linked above, some unexpected clarity Schoenberg’s early music, and in some hidden or emergent kinds of subjects and forms, that Schoenberg seemed to employ before his atonal revolution in 1908.


^1. This concern is relevant to how we hear pulse because musicians spend lots of energy defining and termining timespan lengths in terms of their rational relationships with one another, but they normally do so under an assumption that pulsed frameworks are at least implied. When that framework is removed, “all bets are (or were) off” in our perception of timespan relationships. (I discovered that when simple sequences of timespans, heard in contexts that had no hope of “reinforcing” that simplicity with any contextual metric hierarchy, we still had a tendency to regard those sequences as more orderly than their complex counterparts. And that’s good news for composers who hope their listeners can detect qualities of temporal simplicity or complexity in unmetered music.)

^2. That touches on core aspect of the ‘Wagnerian’ side of this Romantic value system, which is that little tunes (motivs, ideés fixes, themes/tema or subjects/soggetti) are the points of origin not only for developmental narratives, but for musical forms themselves. It could be said that Wagner put the identity of an individual subject at the core of musical processes, seeing whole forms as having been generated from them.


Bregman, A.S. (1990). Auditory scene analysis: the perceptual organization of sound. Cambridge: MIT Press.

Dahlhaus, Carl (1980). “Issues in composition.” In Between Romanticism and Modernism: Four Studies in the Music of the Later Nineteenth Century, 40-78. Translated by Mary Whitall. Berkeley: University of California Press, 1980. 

Deleuze, Gilles, and Félix Guattari (1972). L’Anti-Oedipe, Paris: Editions de Minuit.

Dowling, W.J. (1973). Rhythmic groups and subjective chunks in memory for melodies. Perception and Psychophysics 14(1), 37–40. 

Gregory, A. (1994). Timbre and auditory streaming. Music Perception 12(2), 161–174. 

Idson, W. & Massaro, D. (1976). Cross-octave masking of single tones and musical sequences: the effects of structure on auditory recognition. Perception & Psychophysics 19, 155–175.

Schoenberg, Arnold [originally 1951]. Style and Idea. Translated by Leo Black, with Dika Newlin. Los Angeles: University of California, 1985. Originally published by London: Williams and Norgate, 1951.

_____. [Notes dated 1923-1934, unfinished] The Musical Idea: the Logic, Technique, and Art of its Presentation. Second edition. Edited and translated, with critical commentary by Patricia Carpenter and Severine Neff. Bloomington: Indiana University, 2006.

Tekman, H.G. (1995). Cue trading in the perception of rhythmic structure. Music Perception 13, 17–38.

_____. (1997). Interactions of perceived intensity, duration, and pitch in pure tone sequences. Music Perception 14, 281–294.